Description
This graduate seminar will cover recent research on the use of mathematical programming for problems arising from optimization, machine learning, computational complexity and more, with a particular focus on the "Sum of Squares" semidefinite programming hierarchy. We will discuss both lower and upper bounds, as well as how such mathematical programs give rise to a general theory of computational difficulty, computation vs. sample size tradeoffs, and computational analogs of Bayesian probabilities. The course location will alternate between Harvard and MIT.